Bayesian Inference Approach to Estimate Robin Coefficient using Hybrid Monte Carlo Algorithm

Abstract

In this paper, a non-linear heat conduction problem is considered to identify the Robin coefficient using inverse method. The coefficient of heat transfer represents the corrosion damage, which is time dependent, is estimated for the surrogated data. The forward mathematical model is discretized using finite difference method and implicit scheme is incorporated for temperature time history. A powerful Bayesian framework is applied to obtain the estimates of unknown parameters and the uncertainty associated with the estimated parameter is represented as standard deviation. The sampling space is explored using a Hamiltonian Monte Carlo algorithm. The maximum a posterior, mean and standard deviation are obtained based on 10000 samples. Results prove that Bayesian Inference approach does provide accurate parametric estimation to the inverse heat problem.